There is known a hybrid vehicle having an internal combustion engine and an electric motor such as a motor-generator as power sources, being provided a transmission in a power transmission path between the internal combustion engine and a drive wheel, and being able to switch a connection destination of an output shaft of the motor-generator between an input shaft of the transmission and an output shaft of the transmission by a switching mechanism. As a power transmission control apparatus applied to such the hybrid vehicle, there is known an apparatus to reduce an abrupt change of acceleration of the vehicle by connecting the output shaft of the motor-generator to the output shaft of the transmission and assisting a drive of the drive wheel by the motor generator, when a shift position of the transmission is changed (see Patent Literature 1). In addition, there are Patent Literatures 2-4 as prior art references in relation to the present invention.